From angular momentum hamiltonian to angles(coordinates)

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To transition from a Hamiltonian defined by angular momentum components (Lx, Ly, Lz) to a coordinate representation, one must address the absence of derivatives in the Hamiltonian. The current formulation leads to nonsensical Hamiltonian equations, such as p_i=0. The discussion highlights the need for guidance on converting the Hamiltonian H=-K1Lx^2+K2Lz^2+HxLx+HyLy+HzLz into action-angle variables. While examples exist for systems with coordinates, the challenge lies in handling the angular momentum context. A clear method for this conversion in classical mechanics is sought.
jannyhuggy
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I have a Hamiltonian, consisting only of angular momentum components Lx,Ly,Lz. I need to go from it to some coordinate representation. But I don't have derivatives Lx' etc. in H. So, when I'll go to coordinates and momenta I'll have Hamiltonian equations like p_i=0, which doesn't have sense.
How I need to go from H to x,y,z or \phi,\theta,r.
H=-K1Lx2+K2Lz2+HxLx+HyLy+HzLz

Going from L to angles can make no problem according to https://www.physicsforums.com/showthread.php?t=161865 in example
But back?
 
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Please, somebody! I need at least the guidance how to go in classical case from H=-K1Lx2+K2Lz2+HxLx+HyLy+HzLz to action-angle variables! I know how to do that in a variety examples having coordinates (i.e. harmonic oscillator or Kepler problem etc.) but I don't know what to do having angular momentum in the Hamiltonian! Rewriting via p\cros r doesn't help either!
 

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